Cloth wont stay attached to armature
You need to setup a vertex group for pinned vertices under the cloth modifier, and then assign hooks to the same vertices which go to the respective bones. (May need to move the hooks above cloth in the modifier stack so they take precedence.) That should keep the cloth attached to the rig.

Keep in mind pinning is used for attachment points, so a few around the edges should do it, and the tension in the cloth sim should take care of the rest.